The leader of the Scottish National Party (SNP) denied saying privately that she wanted him to remain in power despite publicly attacking almost everything his Conservative party, which is deeply unpopular in Scotland, stands for.

A leaked memo in The Daily Telegraph newspaper claimed Sturgeon told France's ambassador to Britain that she wanted Cameron to remain prime minister after the May 7 vote.

Britain's top civil servant Jeremy Heywood opened an inquiry into the source of the leak after Sturgeon demanded answers over "such a false account being leaked for transparently political motives".

The allegations are particularly sensitive because Sturgeon, whose party wants independence for Scotland, could play a key role in forming Britain's next government.

With polls predicting no single party will win the election outright, the SNP says it could be prepared to prop up a Labour minority government led by Ed Miliband to keep the Conservatives out.

But some commentators believe that an outright win for the Conservatives could bring another referendum on Scottish independence -- the SNP's defining purpose -- closer.

The memo said: "Discussion appears to have focused mainly on the political situation, with the FM (first minister) stating... that she'd rather see David Cameron remain as PM (and didn't see Ed Miliband as PM material)."

- '100 percent untrue' -

The Telegraph said the leaked note was written by a senior British civil servant following a confidential conversation with Pierre-Alain Coffinier, the French consul-general in Scotland, about Sturgeon's meeting with ambassador Sylvie Bermann in February.

The author of the memo seemed to question the account of Sturgeon's comments, writing: "I'm not sure that the FM's tongue would be quite so loose on that kind of thing in a meeting like that, so it might well be a case of something being lost in translation."

Sturgeon said the story was "categorically 100 percent untrue", while spokespeople for the French embassy and the consul-general also denied it.

She questioned why the story had been leaked to the Conservative-supporting Daily Telegraph, adding that the situation pointed to a "Whitehall system out of control -- a place where political dirty tricks are manufactured and leaked."

The SNP currently has six lawmakers in the House of Commons but is expected to win the majority of Scotland's 59 seats in May, taking many from Labour.

Support for the SNP has surged since Scotland rejected independence at last September's referendum, while Sturgeon also polled strongly for her performance in Thursday's TV leaders debate.

That prompted another Conservative-supporting newspaper, the Daily Mail, to describe her as the "most dangerous woman in Britain" Saturday.

The French embassy's spokesman said: "Ms Sturgeon did not tell the French ambassador about her personal political preferences with regards to the future PM."

Coffinier also denied saying Sturgeon had voiced a preference.

He told AFP: "The political situation in Britain was indeed discussed during the meeting... and I gave a report of it in general terms.

"However, at no stage was a preference expressed about the result of the forthcoming British general election."

Some commentators, though, questioned whether Cameron staying in Downing Street might not be in the SNP's interests.

Fraser Nelson, the Scottish editor of the right-wing Spectator political magazine, wrote that Cameron staying in power "suits the party's wider purpose".

The prime minister has promised to hold a referendum on Britain leaving the EU by 2017 if the Conservatives win on May 7, a move unpopular in Scotland.